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Popular >

derivative of (x-5/(x^2))

Solution

\frac{d}{d x} (\frac{x - 5}{x ^{2}})

Solution

\frac{- x + 10}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x - 5}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x - 5 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x - 5 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x - 5) = 1

\frac{d}{d x} (x^{2}) = 2 x

= \frac{1 \cdot x ^{2} - 2 x ( x - 5 )}{( x ^{2} ) ^{2}}

Simplify

\frac{1 \cdot x ^{2} - 2 x ( x - 5 )}{( x ^{2} ) ^{2}} : \frac{- x + 10}{x ^{3}}

= \frac{- x + 10}{x ^{3}}

Popular Examples

limit as x approaches 6-of cx^2+3x

x \to 6 - lim (c x^{2} + 3 x)

laplacetransform 2y laplace transform

2 y

derivative of (x^2)/(1+x^2)derivative of

\frac{x ^{2}}{1 + x ^{2}}

1/(x^7)y^'=15+12y

\frac{1}{x ^{7}} y^{^{'}} = 15 + 12 y

limit as x approaches 2 of (x-2)/(x-1)

x \to 2 lim (\frac{x - 2}{x - 1})

Frequently Asked Questions (FAQ)

What is the derivative of (x-5/(x^2)) ?
The derivative of (x-5/(x^2)) is (-x+10)/(x^3)
What is the first derivative of (x-5/(x^2)) ?
The first derivative of (x-5/(x^2)) is (-x+10)/(x^3)